Asymptotic behavior of fluctuations for the 1D Ising model in zero-temperature limit

Fluctuation of the average spin for one-dimensional Ising spins with nearest neighbor interactions are studied. The distribution function for the average spin is calculated for a finite volume, finite temperature, and finite magnetic field. As the volume increases and the temperature diminishes at zero magnetic field, there are two limits in which the probability distribution shows quite different behaviors: in the thermodynamic limit as the volume goes to infinity for finite temperature, small deviations of the fluctuations are described by a Gaussian distribution, and in the limit as the temperature vanishes for a finite volume, the ground states are realized with probability one. The crossover between these limits is analyzed via a ratio of the correlation length to the volume. The helix-coil transition in a polypeptide is discussed as an application.     

Triviality of a model of particles with point interactions in the thermodynamic limit

We consider a model of fermions interacting via point interactions, defined via a certain weighted Dirichlet form. While for two particles the interaction corresponds to infinite scattering length, the presence of further particles effectively decreases the interaction strength. We show that the model becomes trivial in the thermodynamic limit, in the sense that the free energy density at any given particle density and temperature agrees with the corresponding expression for non-interacting particles.     

Numerical evidence for critical behavior of the two-dimensional nonequilibrium zero-temperature random field Ising model

We give numerical evidence that the two-dimensional nonequilibrium zero-temperature random field Ising model exhibits critical behavior. Our findings are based on the results of scaling analysis and collapsing of data, obtained in extensive simulations of systems with sizes sufficiently large to clearly display the critical behavior.     

Subcritical asymptotic behavior in the thermodynamic limit of reversible random polymerization processes

We consider a reversible Markov process as a chemical polymerization model and study the asymptotic behavior (in the thermodynamic limit asN+) of a particular probability distribution on the set ofN-dimensional vectors, thekth component of which is the number ofk-mers. The study establishes the existence of three stages (subcritical, near-critical, and supercritical stages) of polymerization, depending on the value of the strength of the fragmentation reaction. The present paper concentrates on the analysis of the subcritical stage. In the subcritical stages we show that the size of the largest length of polymers of sizeN is of the order logN asN+.     

A novel configuration model for random graphs with given degree sequence

Recently, random graphs in which vertices are characterized by hidden variables controlling the establishment of edges between pairs of vertices have attracted much attention. This paper presents a specific realization of a class of random network models in which the connection probability between two vertices (i,j) is a specific function of degrees ki and kj. In the framework of the configuration model of random graphs, we find the analytical expressions for the degree correlation and clustering as a function of the variance of the desired degree distribution. The obtained expressions are checked by means of numerical simulations. Possible applications of our model are discussed.     

Resistance and eigenstates in a tight-binding model with quasiperiodic potential

A one-dimensional tight-binding model on a spatially periodic lattice of lengthN, with quasiperiodic potential strength given by the Fibonacci sequence, is investigated numerically. We elucidate theN-dependence of the resistence and the nature of the wave functions. For energies belonging to the spectrum, the results provide strong evidence for algebraic localization and algebraicN-dependence of the resistance, with a distribution of exponents. Implications for quantum chaos are also discussed.     

Absence of tricritical behavior of the random field Ising model in a honyecomb lattice

In this letter, we study the behavior of the random field Ising model on a honeycomb lattice by means of the effective field theory. We obtain the phase diagram in the T$T$–H$H$ plane for clusters with one spin in a finite size cluster scheme and it is observed the absence of a tricritical point.     

Breather trapping and breather transmission in a DNA model with an interface

We study the dynamics of moving discrete breathers in an interfaced piecewise DNA molecule. This is a DNA chain in which all the base pairs are identical and there exists an interface such that the base pairs dipole moments at each side are oriented in opposite directions. The Hamiltonian of the Peyrard-Bishop model is augmented with a term that includes the dipole-dipole coupling between base pairs. Numerical simulations show the existence of two dynamical regimes. If the translational kinetic energy of a moving breather launched towards the interface is below a critical value, it is trapped in a region around the interface collecting vibrational energy. For an energy larger than the critical value, the breather is transmitted and continues travelling along the double strand with lower velocity. Reflection phenomena never occur. The same study has been carried out when a single dipole is oriented in opposite direction to the other ones. When moving breathers collide with the single inverted dipole, the same effects appear. These results emphasize the importance of this simple type of local inhomogeneity as it creates a mechanism for the trapping of energy. Finally, the simulations show that, under favorable conditions, several launched moving breathers can be trapped successively at the interface region producing an accumulation of vibrational energy. Moreover, an additional colliding moving breather can produce a saturation of energy and a moving breather with all the accumulated energy is transmitted to the chain.     

Conductance of a single-wall carbon nanotube in a one-parameter tight-binding model

The dependence of current-voltage characteristics of single-wall nanotubes on their radius and chirality is studied theoretically. It is shown that the conductance of a single-wall nanotube at low voltages can assume discrete values equal to zero for a dielectric tube and 4(e²/h) for a conducting tube (e is the electron charge, h is the Planck constant). The current-voltage characteristic of a nanotube exhibits kinks related to the discreteness of the electron spectrum. The behavior of the conductance of the nanotube at zero temperature is analyzed in a quantizing longitudinal magnetic field that changes the type of tube conduction. In a magnetic field, the conductance of a dielectric tube at low voltages can assume a value of 2(e²/h) in the region where the tube becomes conducting. In a weak magnetic field, a conducting tube becomes dielectric with an energy gap depending on the magnitude of the magnetic field. The conductance of a carbon nanotube is calculated as a function of the temperature and longitudinal magnetic field.     

Absence of symmetry breaking for systems of rotors with random interactions

We prove that Gibbs states for the Hamiltonian , with thes _x varying on theN-dimensional unit sphere, obtained with nonrandom boundary conditions (in a suitable sense), are almost surely rotationally invariant if withJ _xy i.i.d. bounded random variables with zero average, 1 in one dimension, and 2 in two dimensions.     

Convergence to the ground-state energy in the thermodynamic limit of the Ising model in a strong transverse field

For the quantum mechanical Ising model in a strong transverse field we show that the convergence of the ground-state energy per site as the volume goes to infinity has an Ornstein-Zernicke behavior. That is, if the diameter of thed-dimensional lattice is given byL, the absolute value of the difference of the ground-state energy per site and its limit is asymptotically exp(-L)L ^–d/2 for some positive constant. We also show that the correlation function has the same behavior. Our results are derived by cluster expansions, using a method of Bricmont and Fröhlich which we extend to the quantum mechanical case.     

On the existence of the thermodynamic limit for classical systems with nonspherical potentials

It is shown, that the configurational partition function for a classical system of molecules interacting with nonspherical pair potential is proportionals to the configurational partition function for a system of particles interacting with temperature-dependent spherical k-body potentials (k ?2). Therefore, the thermodynamic limit for nonspherical molecules exists if the effective k-body interaction is stable and tempered. A number of criteria for the nonspherical potential are developed which ensure these properties. In case the nonsphericity is small in a certain sense, stability and temperedness of the angle-averaged nonspherical potential are sufficient to ensure thermodynamic behaviour.     

Thermodynamic limit for the one-dimensional Ising systems with random interaction of finite range

The existence of the thermodynamic limit is proved for the random one-dimensional Ising systems under the assumption that the interaction energies are random variables taking on continuous values and the distribution of the random variables is given by a continuous function. It is assumed that the total number of possible configurations for each lattice site is finite and the range of interaction is finite.